Try the free trials of all of them. Aperture, lightroom, and Photoshop Elements all have them. As noted earlier, GIMP is free.

I would call myself and enthusiastic hobbiest. Lightroom and Aperture are nearly a wash in my opinion besides price and some differences (most obvious: 3rd party add-ons available for Aperture). I found that I like Aperture because it interacts so well with the rest of the Mac programs and adds more control of photos than iPhoto. I have GIMP, but am pretty amateur with it. I haven't found the need to play with layers in my photos much yet, and Aperture has met most of my editing needs. I can't justify the price of Photoshop unless I begin to sell/work in photography. I tried Photoshop Elements. It's interface with iPhoto was a bit choppy (confusing switching into PE from iPhoto to edit and then going back), it interacted with Aperture flawlessly. PE seemed to be a large program though with several components (Bridge, which I didn't see the need for with if you are organizing with another program; Camera RAW).

Lengthy, but my advice is try them all for free. Play with how they interact with each other and other programs on your Mac. Consider your needs and program prices (ie. for ~$80 P. Elements my cover all your needs for organizing, editing, etc.).